Continuity mistake: When Doug goes to get Carrie's present from the closet her position on the bed changes between shots. (00:05:30)
Hi Def-Jam - S3-E13
Continuity mistake: At the start Carrie is holding an egg in two hands or one hand depending on the camera angle. (00:00:42)
Strike Too - S3-E6
Continuity mistake: At the start when Doug is having his breakfast something appears on top of his pancakes. (00:00:30)
Strike Too - S3-E6
Continuity mistake: When Carrie puts her bag on at the start it swaps arms instantly. (00:02:30)
Continuity mistake: When Danny interrupts Deacon and Kelly's dinner the couple retreat to their bedroom, and while Spence mumbles to himself as he clears the plates, in the closeup he places some plates on the pass-through shelf, but those plates have vanished in the next wide shot.
Maybe Baby - S1-E25
Continuity mistake: When Doug tells Deacon that he and Carrie are trying for a baby, Deacon has both hands on his knees, camera changes and he's got 1 hand and 1 elbow on his knees. (00:09:50)
Continuity mistake: When Danny storms out he is not through the door - the camera changes and the door is closed and Danny is gone. (00:18:20)
Continuity mistake: When Arthur is listing the genres of the film, his legs go from on the floor to one raised and back between shots. (00:02:10)
Taste Buds - S5-E24
Continuity mistake: Just after Carrie tells Doug that she knows what he has been doing, she storms out of the kitchen. Doug has his hand on a water bottle on the table, then picks it up as he rushes after Carrie. In the next shot of Doug walking into the living room, the water bottle is gone.
Fixer Upper - S1-E12
Continuity mistake: At the start, the items in Carrie's hands swap hands instantly. (00:00:10)
Continuity mistake: When the guy chucks his cheque book into the basket, it reappears in his hand a second later. (00:11:20)
Road Rayge - S1-E9
Continuity mistake: When driving Doug home, look out the back window to see 2 red car lights appear instantly and out of nowhere. (00:12:20)
Road Rayge - S1-E9
Continuity mistake: When trying to get Doug to drive after the Jets' game, Ray's press pass goes from white to green instantly. (00:09:20)
Continuity mistake: In the first classroom scene there are two people sat to Doug's right. These people then vanish a few seconds later. (00:07:55)
Continuity mistake: While Arthur tries to convince Spence about the card, when Spence bites into the fake cookie he's holding it in his left hand and holding the plate in his right hand, but in the next shot facing Arthur the items have switched hands. (00:16:30)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.